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Calculus by Gilbert Strang

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Calculus written by Gilbert Strang, Massachuselts Institute of Technology.

Calculus written by Gilbert Strang cover the following topics.

  • Introduction to Calculus
    Velocity and Distance, Calculus Without Limits, The Velocity at an Instant, Circular Motion, A Review of Trigonometry, A Thousand Points of Light, Computing in Calculus
  • Derivatives
    The Derivative of a Function, Powers and Polynomials, The Slope and the Tangent Line, Derivative of the Sine and Cosine, The Product and Quotient and Power Rules, Limits, Continuous Functions
  • Applications of the Derivative
    Linear Approximation, Maximum and Minimum Problems, Second Derivatives: Minimum vs. Maximum, Graphs, Ellipses, Parabolas, and Hyperbolas, Iterations x,+ ,= F(x,), Newton's Method and Chaos, The Mean Value Theorem and l'H8pital's Rule
  • The Chain Rule
    Derivatives by the Chain Rule, Implicit Differentiation and Related Rates, Inverse Functions and Their Derivatives, Inverses of Trigonometric Functions,
  • Integrals
    The Idea of the Integral, Antiderivatives, Summation vs. Integration, Indefinite Integrals and Substitutions, The Definite Integral, Properties of the Integral and the Average Value, The Fundamental Theorem and Its Consequences, Numerical Integration

  • Exponentials and Logarithms
    An Overview, The Exponential ex, Growth and Decay in Science and Economics, Logarithms, Separable Equations Including the Logistic Equation, Powers Instead of Exponentials, Hyperbolic Functions

  • Techniques of Integration
    Integration by Parts, Trigonometric Integrals, Trigonometric Substitutions, Partial Fractions, Improper Integrals

  • Applications of the Integral
    Areas and Volumes by Slices, Length of a Plane Curve, Area of a Surface of Revolution, Probability and Calculus, Masses and Moments, Force, Work, and Energy

  • Polar Coordinates and Complex Numbers
    Polar Coordinates, Polar Equations and Graphs, Slope, Length, and Area for Polar Curves, Complex Numbers

  • Infinite Series
    The Geometric Series, Convergence Tests: Positive Series, Convergence Tests: All Series, The Taylor Series for ex, sin x, and cos x, Power Series

  • Vectors and Matrices
    Vectors and Dot Products, Planes and Projections, Cross Products and Determinants, Matrices and Linear Equations, Linear Algebra in Three Dimensions

  • Motion along a Curve
    The Position Vector, Plane Motion: Projectiles and Cycloids, Tangent Vector and Normal Vector, Polar Coordinates and Planetary Motion

  • Partial Derivatives
    Surfaces and Level Curves, Partial Derivatives, Tangent Planes and Linear Approximations, Directional Derivatives and Gradients, The Chain Rule, Maxima, Minima, and Saddle Points

  • Constraints and Lagrange Multipliers
    Multiple Integrals, Double Integrals, Changing to Better Coordinates, Triple Integrals, Cylindrical and Spherical Coordinates

  • Vector Calculus
    Vector Fields, Line Integrals, Green's Theorem, Surface Integrals, The Divergence Theorem, Stokes' Theorem and the Curl of F

  • Mathematics after Calculus
    Linear Algebra, Differential Equations, Discrete Mathematics, Study Guide For Chapter 1, Answers to Odd-Numbered Problems

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